Validation of the Thermal Modeling Process for Cold-Chain Shippers

One company shows a strong parallel between phase change simulations and actual data.

In “Bringing Cold Chain Shippers to Market Faster with Thermal Modeling” (Pharmaceutical & Medical Packaging News, May 2008), we discussed Cold Chain Technologies’ (CCT) use of predictive thermal modeling to simulate multiple design scenarios to arrive at an optimal configuration before making prototypes and conducting chamber testing. A computer program used during the modeling process lets the user pass through a number of required steps, including analysis selection, geometry creation, element selection, boundary condition application, and program execution.

As this modeling process makes certain approximations and assumptions, model validation must occur before the process can be confidently utilized over CCT’s full array of products. This article discusses the thermal modeling validation process that is being undertaken by CCT to accomplish this task, along with some of its initial results.

Thermal Modeling Validation Method

To successfully simulate thermal packaging, modeling (and validation) of the complete transient thermal response must be completed. This validation process includes, but is not limited to, the following coupled areas:

• Phase change of refrigerant(transient).

• Free convection in shipper (transient).

• Conduction in shipper (transient).

• Payload geometry approximations.

• Material properties of shipper components.

By validating each of the above areas separately, the complete thermal package can be simulated with much more certainty. In general, the validation process consists of the following steps:

Phase Change Experiment. A robust modeling process needs accurate simulations of phase change in thermal shippers. The phase change validation process began by designing a simple, controlled experiment to model the phase change process in a similar way to what actually occurs during shipping. In one experiment, two CCT water-based foam bricks (CCT 316F, 7 × 5 × 1 in.) were placed back-to-back, with three thermocouples (TCs) in between them, and secured together. This approach eliminates the need to insert the TCs directly into the frozen bricks, and makes exact TC geometric location easy to control. The taped brick assembly was placed into an environmental chamber at –20ºC, and once all three TCs verified that the bricks were completely frozen, the assembly was suspended in a temperature-controlled (ambient, 22ºC) chamber with the configuration and direction of gravity as shown in Figure 1.

The thermal response of the brick assembly, including phase change, was measured via TC, at the locations shown in Figure 1, namely: a) 1 in. from the bottom left corner, b) the absolute geometric center, and c) the midpoint between the geometric center and the top edge. The data were collected, and temperature versus time graphs were constructed for each of the three TCs and the chamber (ambient).

Phase Change Simulation and Comparison of Results. The brick geometry was generated via solid modeling software and input into the analysis program, along with the thermal properties—density, specific heat, and thermal conductivity—of solid ice. To account for phase change from solid ice to liquid water, thermal conductivity and specific heat variation with temperature were input into the program, along with the corresponding latent heat of fusion. The brick geometry was meshed using solid elements. The air surrounding the brick was assigned room temperature properties and meshed using fluid elements (perfect thermal contact was assumed between the two bricks).

Table 1: The location of each thermocoupling shown in Figure 1 can be referenced here.
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A 3-D transient thermal model, including both conduction and free convection was then executed. To replicate the above testing conditions, an initial condition of –20ºC was assigned to the entire solid brick volume, and an initial air temperature of 22ºC was assigned to the brick surroundings. The transient model was run for 14 hours, saving data every hour. Variations of fluid volume, brick mesh size, and solver time step were completed to determine a satisfactory trade off between accuracy and solve time. The results of the simulation, and the corresponding actual data for the three TC locations “A”, “B”, and “C” are shown in Figures 2a, 2b, and 2c, respectively.

As shown in the figures, the agreement between the actual TC data and the simulation results is reasonably good. The ramp rate from –20º to 0ºC and the phase change time for each TC location are close to actual data. As the phase change time is of critical importance, these initial results are certainly promising.

Figure 2a: Foam Brick Phase Change Data vs. Simulation for TC location “A.” The agreement between the actual TC data and the simulation shows the phase change time for each TC location are close to actual data.
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Figure 2b: Foam Brick Phase Change Data vs. Simulation for TC location “B.” Here, and in Figure 2a, the values of the simulations at the end of phase change are higher than actual data, but the trends appear correct.
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Figure 2c: Foam Brick Phase Change Data vs. Simulation for TC location “C.” Here the shape of the simulated phase change curve at the end of phase change is not accurate compared to actual data.
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To improve upon the simulation, however, deviations with actual data must be analyzed and corrected via compounding. In TC locations A and B, for example, the values of the simulations at the end of phase change are higher than actual data, but the trends appear to be correct. In location C the shape of the simulated phase change curve at the end of phase change does not match the actual data. These deviations can be explained by considering the material properties input into the analysis program. Specifically, the variation in specific heat with temperature was input into the program as a “step” function (one value for solid that is switched to a different value for liquid).

In reality, the specific heat versus temperature will be smooth, showing much more of a curve. As such, the shape of the transient simulation curve will tend to “mirror” the specific heat versus temperature curve input into the program. Specific heat versus temperature data are being generated at CCT, as part of the model validation process, and will be used during future simulation runs to further compound and validate the model.

Experiments, similar to refrigerant phase change described above, are being designed to extend the validation process to:

• Free convection.

• Conduction.

• Payload geometry.

• Material properties.

Free convection and conduction experiments will involve the use of simple geometry, known boundary conditions and initial conditions via thermal chamber, and continually improved material properties. Steady-state analysis will be used whenever possible. Payload geometry experiments will be completed and followed by simulation to determine the relative importance of free convection and conduction. The overall goal is to find how much detail is needed for solid modeling of the product load to obtain satisfactory results. Material property determination will include all key transient thermal characteristics—thermal conductivity, specific heat, and density—for the range of components used at CCT such as shippers, refrigerants, corrugate, and dunnage. It should be noted, too, that the above phase change validation process did incorporate free convection, even though that was not the focus of the validation work. This fact provides additional evidence for the robustness of the thermal modeling techniques being used by CCT.

Comparison of simulation results and actual chamber test data has shown that CCT now has the capability to reliably model phase change of its refrigerants in a stagnant air (free convection) environment. Additional phase change model compounding will be completed as material properties (for example, specific heat versus temperature) are further developed. In addition, this validation process can, and will be, extended to other key areas for shipper simulation, including free convection, conduction, payload geometry, and material properties. Once simulation of each of these individual areas has been completed, validation of total representative shipper solutions will follow.